A Differential Evolution Algorithm for Multi-objective Sparse Reconstruction

Aims: This paper proposes a differential evolution algorithm to solve the multi-objective sparse reconstruction problem (DEMOSR). Background: The traditional method is to introduce the regularization coefficient and solve this problem through a regularization framework. But in fact, the sparse reconstruction problem can be regarded as a multi-objective optimization problem about sparsity and measurement error (two contradictory objectives). Objective: A differential evolution algorithm to solve multi-objective sparse reconstruction problem (DEMOSR) in sparse signal reconstruction and the practical application. Methods: First of all, new individuals are generated through tournament selection mechanism and differential evolution. Secondly, the iterative half thresholding algorithm is used for local search to increase the sparsity of the solution. To increase the diversity of solutions, a polynomial mutation strategy is introduced. Results: In sparse signal reconstruction, the performance of DEMOSR is better than MOEA/D-ihalf and StEMO. In addition, it can verify the effectiveness of DEMOSR in practical applications for sparse reconstruction of magnetic resonance images. Conclusions: According to the experimental results of DEMOSR in sparse signal reconstruction and the practical application of reconstructing magnetic resonance images, it can be proved that DEMOSR is effective in sparse signal and image reconstruction.